In this post we will see the book The Theory of Functions of A Complex Variable by A. G. Sveshnikov and A. N. Tikhonov.

About the book

The book covers basic aspects of complex numbers, complex variables and complex functions. It also deals with analytic functions, Laurent series etc.

The book was translated from the Russian by Eugene Yankovsky and was first published by Mir in 1971 with a reprint in 1973. The current book is the second edition first published in 1978 and reprinted in 1982.

Contents

1.1. Complex Numbers and Operations on Complex Numbers 11
a. The concept of a complex number 11
b. Operations on complex numbers 11
c. The geometric interpretation of complex numbers 13
d. Extracting the root of a complex number 15

1.2. The Limit of a Sequence of Complex Numbers 17
a. The definition of a convergent sequence 17
b. Cauchy’s test 19
c. Point at infinity 19

8.2. Determining the Original Function from the Transform 238
a. Mellin’s formula 238
h. Existence conditions of the original function 241
c. Computing the Mellin integral 245
d. The case of a function regular at infinity 249